Some nuclei possess angular momentum or spin and can be thought of as tiny spinning particles. Bearing charges, the spinning nuclei produce a magnetic moment, or a field, that is similar to that created by a microscopic bar magnet. When placed in a steady external magnetic field, the net magnetic moments of a collection of such nuclei attempt to line up with the magnetic field. Some nuclei align themselves parallel to the magnetic field B.sub.0 while others align themselves antiparallel to the magnetic field B.sub.0. These two different orientations have different energies. The number of nuclei in the high and low energy states at equilibrium follows a Boltzman distribution, the population difference being inversely related to the energy difference between the two stales. At equilibrium, more nuclei will be in the low energy state than in the high energy state. The individual magnetic dipoles, however, cannot line up with the external magnetic field, but rather are tilted at an angle to the magnetic field. Tilted at an angle, the dipoles will precess at an angle about the imposed magnetic field axis at a particular frequency, known as the Larmor frequency. The Larmor frequency (f.sub.0) is related to the magnetic field B.sub.0 at the nucleus by the equation f.sub.0 =.gamma.B.sub.0 /2.pi., where .gamma., a constant, is the magnetogyric ratio of each nuclear species.
If external electromagnetic radiation (typically pulses in the radio frequency ("rf") range) is applied to the nuclei at the Larmor frequency, a resonance occurs, whereby the rf energy is absorbed due to the excess spin population of nuclei in the low energy state, causing the magnetic moments in the lower energy state (for example parallel) to flip to the higher energy state (for example antiparallel). Depending on the duration of the rf pulse in pulsed NMR, the populations of the two levels will be perturbed from the equilibrium populations, and may become equal (90.degree. pulse) or even inverted (180.degree. pulse). When the pulsed irradiation ceases, the precession of magnetic moments can be detected by a receiver coil. The populations of parallel and antiparallel nuclei return to an equilibrium state with a characteristic time period T.sub.1, also known as the nuclear spin-lattice or longitudinal relaxation time.
Different nuclei precess at different frequencies and, therefore, at a particular magnetic field strength, the nuclei will generally absorb energy at certain characteristic radio frequencies. Also, nuclei of the same nuclear species will absorb energy at slightly different frequencies, depending upon their molecular environment. Further, if the sample is a solid, the crystallographic orientation of the sample (the position of the crystal axes, or molecular axes for non-crystalline materials, relative to a magnetic field) can also affect the frequency of absorption.
In liquid samples, highly accurate NMR absorption frequencies can be determined due to the random tumbling and rapid reorientation of sample molecules in solution, This rapid reorientation effectively causes the surroundings of the resonating nuclei to appear isotropic on the time scale of the NMR experiment, and sharp absorption peaks can be obtained.
If polycrystalline, powdery, glassy, amorphous, sintered, or other solids in which the axes of individual chemical bonds in the sample are oriented at random are studied, however, observable peaks or lines are generally broadened due to different orientations of the axes with respect to the external magnetic field B.sub.0. That is, the crystallites in a powder, for example, may be arranged randomly such that only a small number of axes have an orientation with a corresponding resonance frequency matching the input radio frequency, i.e., only a small number may be brought into resonance for any particular radio frequency. Even when so-called "pulsed" Fourier-transform (FT) methods are used, only a limited frequency range can be excited and observed in many cases of practical interest, such as 14N NMR.
In such situations, one way to help eliminate the sensitivity loss due to reduced numbers of resonating nuclei is to repeatedly scan the sample and add the results of each scan. As an increasing number of scans are added the signal portion of the summed scans increases more rapidly than the noise. This is because the signal increases linearly with the number of scans, while the noise increases proportionally to the square root of the number of scans. Thus, as more and more scans are added, absorption peaks can be discerned with a signal-to-noise ratio increasing as the square root of the number of scans.
The principal drawback with this approach is that the user must wait a time period comparable to the spin-lattice relaxation time of the sample before performing another scan in order to obtain the sensitivity advantage from multiple scan acquisitions. For spin-lattice relaxation times on the order of minutes, the amount of time required to acquire the requisite number of scans can be inordinately long. (Of course, the times depend on a number of factors, including, but not limited to nucleus, type of solid samples, and magnetic field strength of spectrometer.)
A second difficulty in applying NMR spectroscopy to such samples (hereafter referred to as "crystallites," although the samples may be amorphous, glassy, disordered, sintered, etc.) in the regime where the rf irradiation is sufficient only to observe a portion of the entire spectrum at one time is that one often wishes to know the appearance of the entire spectrum. This appearance is affected by the magnitude of the orientation dependent NMR interaction parameters. If the external magnetic field strength is fixed, the rf frequency must be changed in a multitude of relatively small steps. The probe may also need to be returned before acquiring multiple scans at each frequency, resulting in a time-consuming procedure that is difficult to automate,